ECAT Pre Engineering Entry Test With Answers

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ECAT Pre Engineering Entry Test

Sr. # Questions Answers Choice
1 A coin is tossed. If head comes up, a die is thrown but if tail comes up, the coin is tossed again. The probability of obtaining a head and an even number is 1/8 2/8 3/8 None of these
2 An unbiased die is thrown. Then the probability of getting a prime is 1/2 2/3 3/4 None of these
3 Three unbiased coins are tossed. Then the probabilities of getting two heads is 3/8 1/8 1/4 None of these
4 Two balanced dice are tossed once, the sample space when the integers on the faces of two dice are the same is {(1, 1), (2, 2), (3, 3)} {(4, 4), (5, 5), (6, 6)} {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)} None of these
5 The number of divisors of 1029, 1547 and 122 are in A.P. G.P. H.P. None of these
6 The number of divisors of 1029, 1547 and 122 are in A.P. G.P. H.P. None of these
7 Let the sequence 1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, ..... where n consecutive terms have the value n, then 1025th term is 2<sup>9</sup> 2<sup>10</sup> 2<sup>11</sup> 2<sup>8</sup>
8 An A.P., a G.P. and a H.P. have the same first and last terms and the same odd numbers of terms, the middle terms of the three series are in A.P. G.P. H.P. None of these
9
10 1/2 2 1/4 4
11 The sum of the squares of three distinct real numbers, which are in G.P., is S2. if their sum isαS then
12
13 The third term of a G.P. is the square of first term. If the second term is 8, then the 6th term is 120 124 128 132
14 Three consecutive terms of a progression are 30, 24, 20. The next terms of the progression is
15 If b1, b2, b3, ... are in G.P. with first term unity and common ratio r, then the minimum value of b1- b3+ b5is equal to 3/4 1/4 1 None of these
16 The 10th common term between the series 3+7+11+....... and 1 + 6 +11 + ....... is 191 193 211 None of these
17 Let a1, a2, a3, a4and a5be such that a1, a2, and a3are in A.P., a2, a3and a4are in G.P and a3, a4and a5are in H.P. Then, a1, a3and a5are in G.P. A.P. H.P. None of these
18 If three unequal numbers p, q, r are in H.P. and their squares are in A.P., then the ration p : q : r is
19 The consecutive terms of a progressions are 30, 24, 20. The next term of the progression is
20 Every term of a G.P. is positive and also every term is the sum of two preceding terms. Then the common ratio of the G.P. is
21 2<sup>2</sup>- n - 1 1 - 2<sup>-n</sup> n + 2<sup>-n</sup>-1 2<sup>n</sup>- 1
22 If a, b, c are in AP., a, b, c are in G.P. then A, m2b, c are in A.P. G.P. H.P. None of these
23 If a1= a2= 2, an= an-1- 1 (n > 2), then a5is 1 0 -1 -2
24 pth term of an H.P. is qr and qth term is pr then the rth term of the H.P. is pqr 1 pq pqr<sup>2</sup>
25 If the pth, qth, and rth terms of an A.P. are in G.P:., then the common ratio of the G.P. is
26 1 2 3/2 5/2
27
28 If P, Q, R be the A.M., G.M., H.M. respectively between any two rational numbers a and b, then P - Q is
29 99th term of the series 2 + 7 + 14 + 23 + 34 + ..... is 9998 9999 10000 None of these
30 A.P. G.P. H.P. None of these
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